Quantification of truncation errors in minimal cut set-based fault tree analysis

Abstract

Fault tree analysis is extensively and very successfully used in nuclear, chemical, aerospace industries and in other high-risk situations. Its efficacy is gained primarily when it is integrated with the event tree analysis as a part of the probabilistic safety assessment (PSA). PSA has also contributed significantly to the understanding of the safety of nuclear power plants. The majority of fault tree analysis methods are based on the minimal cut set (MCS) approach. However, in MCS-based fault tree analyses, it is impossible to enumerate all the cut sets of a very large tree due to high memory requirements and long computing time. To determine a set of MCSs with a manageable size, truncation neglecting low-probability cut sets is usually applied. The application of the truncation entails the need to estimate the truncation error, i.e., the additional probability of system failure related to the discarded cut sets. In general, the final truncation limits are established by an iterative process of demonstrating that the overall results are not significantly changed and no important accident sequences are inadvertently eliminated. Thus the problem of accurately estimating the truncation error is important. In this study, the mathematical formulation of the truncation error is presented and a practical method to estimate the truncation error has been developed. The proposed truncation error evaluation method is based on an efficient Monte Carlo algorithm using the characteristics of the truncation error, the dagger sampling method and the importance sampling technique. The proposed truncation error evaluation method can be easily applied to most problems in PSAs and does not require much computing time for a good truncation error evaluation. In MCS-based fault tree analysis, there are two quantification uncertainties due to the truncation neglecting low-probability cut sets and the approximation in quantifying minimal cut sets (MCSs). In order to exactly q...